Author: Yumei Dang
Publisher: World Scientific
ISBN: 9810232969
Category : Mathematics
Languages : en
Pages : 163
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Book Description
Includes an interactive tour of the space of hypercomplex Julia sets and an educational mini-documentary introducing fractals and hypercomplex geometry.
Author: Andrzej Katunin
Publisher: CRC Press
ISBN: 1351801201
Category : Computers
Languages : en
Pages : 104
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Book Description
This book presents concisely the full story on complex and hypercomplex fractals, starting from the very first steps in complex dynamics and resulting complex fractal sets, through the generalizations of Julia and Mandelbrot sets on a complex plane and the Holy Grail of the fractal geometry – a 3D Mandelbrot set, and ending with hypercomplex, multicomplex and multihypercomplex fractal sets which are still under consideration of scientists. I tried to write this book in a possibly simple way in order to make it understandable to most people whose math knowledge covers the fundamentals of complex numbers only. Moreover, the book is full of illustrations of generated fractals and stories concerned with great mathematicians, number spaces and related fractals. In the most cases only information required for proper understanding of a nature of a given vector space or a construction of a given fractal set is provided, nevertheless a more advanced reader may treat this book as a fundamental compendium on hypercomplex fractals with references to purely scientific issues like dynamics and stability of hypercomplex systems.
Author: Daniel S. Alexander
Publisher: American Mathematical Soc.
ISBN: 0821844644
Category : Mathematics
Languages : en
Pages : 474
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Book Description
The theory of complex dynamics, whose roots lie in 19th-century studies of the iteration of complex function conducted by Koenigs, Schoder, and others, flourished remarkably during the first half of the 20th century, when many of the central ideas and techniques of the subject developed. This book paints a robust picture of the field of complex dynamics between 1906 and 1942 through detailed discussions of the work of Fatou, Julia, Siegel, and several others.
Author: Richard L Amoroso
Publisher: World Scientific
ISBN: 9814468576
Category : Science
Languages : en
Pages : 510
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Book Description
Author: Richard L Amoroso
Publisher: World Scientific
ISBN: 9814462950
Category : Science
Languages : en
Pages : 412
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Book Description
The Maxwell, Einstein, Schrödinger and Dirac equations are considered the most important equations in all of physics. This volume aims to provide new eight- and twelve-dimensional complex solutions to these equations for the first time in order to reveal their richness and continued importance for advancing fundamental Physics. If M-Theory is to keep its promise of defining the ultimate structure of matter and spacetime, it is only through the topological configurations of additional dimensionality (or degrees of freedom) that this will be possible. Stretching the exploration of complex space through all of the main equations of Physics should help tighten the noose on “the” fundamental theory. This kind of exploration of higher dimensional spacetime has for the most part been neglected by M-theorists and physicists in general and is taken to its penultimate form here.
Author: Pradip Debnath
Publisher: Springer Nature
ISBN: 9811648964
Category : Mathematics
Languages : en
Pages : 356
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Book Description
This book collects chapters on contemporary topics on metric fixed point theory and its applications in science, engineering, fractals, and behavioral sciences. Chapters contributed by renowned researchers from across the world, this book includes several useful tools and techniques for the development of skills and expertise in the area. The book presents the study of common fixed points in a generalized metric space and fixed point results with applications in various modular metric spaces. New insight into parametric metric spaces as well as study of variational inequalities and variational control problems have been included.
Author: Yumei Dang
Publisher:
ISBN:
Category :
Languages : en
Pages : 294
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Book Description
Author: Abdulla Azamov
Publisher: Springer
ISBN: 3030014762
Category : Mathematics
Languages : en
Pages : 197
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Book Description
This book features papers presented during a special session on dynamical systems, mathematical physics, and partial differential equations. Research articles are devoted to broad complex systems and models such as qualitative theory of dynamical systems, theory of games, circle diffeomorphisms, piecewise smooth circle maps, nonlinear parabolic systems, quadtratic dynamical systems, billiards, and intermittent maps. Focusing on a variety of topics from dynamical properties to stochastic properties of dynamical systems, this volume includes discussion on discrete-numerical tracking, conjugation between two critical circle maps, invariance principles, and the central limit theorem. Applications to game theory and networks are also included. Graduate students and researchers interested in complex systems, differential equations, dynamical systems, functional analysis, and mathematical physics will find this book useful for their studies. The special session was part of the second USA-Uzbekistan Conference on Analysis and Mathematical Physics held on August 8-12, 2017 at Urgench State University (Uzbekistan). The conference encouraged communication and future collaboration among U.S. mathematicians and their counterparts in Uzbekistan and other countries. Main themes included algebra and functional analysis, dynamical systems, mathematical physics and partial differential equations, probability theory and mathematical statistics, and pluripotential theory. A number of significant, recently established results were disseminated at the conference’s scheduled plenary talks, while invited talks presented a broad spectrum of findings in several sessions. Based on a different session from the conference, Algebra, Complex Analysis, and Pluripotential Theory is also published in the Springer Proceedings in Mathematics & Statistics Series.
Author: Howard Bloom
Publisher: Prometheus Books
ISBN: 1616145528
Category : Religion
Languages : en
Pages : 714
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Book Description
God’s war crimes, Aristotle’s sneaky tricks, Einstein’s pajamas, information theory’s blind spot, Stephen Wolfram’s new kind of science, and six monkeys at six typewriters getting it wrong. What do these have to do with the birth of a universe and with your need for meaning? Everything, as you’re about to see. How does the cosmos do something it has long been thought only gods could achieve? How does an inanimate universe generate stunning new forms and unbelievable new powers without a creator? How does the cosmos create? That’s the central question of this book, which finds clues in strange places. Why A does not equal A. Why one plus one does not equal two. How the Greeks used kickballs to reinvent the universe. And the reason that Polish-born Benoît Mandelbrot—the father of fractal geometry—rebelled against his uncle. You’ll take a scientific expedition into the secret heart of a cosmos you’ve never seen. Not just any cosmos. An electrifyingly inventive cosmos. An obsessive-compulsive cosmos. A driven, ambitious cosmos. A cosmos of colossal shocks. A cosmos of screaming, stunning surprise. A cosmos that breaks five of science’s most sacred laws. Yes, five. And you’ll be rewarded with author Howard Bloom’s provocative new theory of the beginning, middle, and end of the universe—the Bloom toroidal model, also known as the big bagel theory—which explains two of the biggest mysteries in physics: dark energy and why, if antimatter and matter are created in equal amounts, there is so little antimatter in this universe. Called "truly awesome" by Nobel Prize–winner Dudley Herschbach, The God Problem will pull you in with the irresistible attraction of a black hole and spit you out again enlightened with the force of a big bang. Be prepared to have your mind blown. From the Hardcover edition.
Author: Danilo P. Mandic
Publisher: John Wiley & Sons
ISBN: 0470742631
Category : Science
Languages : en
Pages : 344
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Book Description
This book was written in response to the growing demand for a text that provides a unified treatment of linear and nonlinear complex valued adaptive filters, and methods for the processing of general complex signals (circular and noncircular). It brings together adaptive filtering algorithms for feedforward (transversal) and feedback architectures and the recent developments in the statistics of complex variable, under the powerful frameworks of CR (Wirtinger) calculus and augmented complex statistics. This offers a number of theoretical performance gains, which is illustrated on both stochastic gradient algorithms, such as the augmented complex least mean square (ACLMS), and those based on Kalman filters. This work is supported by a number of simulations using synthetic and real world data, including the noncircular and intermittent radar and wind signals.
